The Board

This 3D variant is played on a board that is basically 4x3x3, with the
long axis oriented so that it points toward the players. Call the horizontal
layers A (the top), B, and C, the vertical faces with a row orientation
1 through 4, and the vertical side-faces (column orientation) a, b, and
c. There are two additional squares -- B0b and B5b -- extending from the
end faces.

Each player starts the game with 10 pieces: a king, three pawns, three
rooks, and three bishops. None of them move in exactly the expected manner,
however. The names are merely for convenience. Here is the initial arrangement:

Top layer
(A)
4: b r b
3: - - -
2: - - -
1: B R B

Middle layer
(B)
5: k
4: r p r
3: - - -
2: - - -
1: R P R
0: K

Bottom layer
(C)
4: p b p
3: - - -
2: - - -
1: P B P

The Rules

There are two ways to win Cube+: Either checkmate the opposing king,
or move a piece into the opponent's extension square (the one on row 0
or 5) without it being subject to immediate capture.

The rook moves exactly one square left or right, forward or back, or
up or down. It captures as it moves.

The king moves and captures in the same manner as the rook, with the
usual prohibition on moving into check.

The bishop moves exactly one square diagonally within any two-dimensional
plane, but not along the 3D diagonals (from B3b to B4a, B4c, B2a, or B2c;
A3a, A3c, A4b, or A2b; or C3a, C3c, C4b, or C2b; but NOT from B3b to A4a,
etc.). The bishop captures as it moves. Note that one player starts the
game with two white bishops and one black bishop, the other with two black
bishops and one white bishop. This might lead to a fairly interesting strategic
imbalance.

The pawn moves like a Cube+ rook and captures like a Cube+ bishop. There
is no pawn promotion, and pawn movement exhibits no directional bias; the
pawn can move or capture forward or backward, up or down. Here is the pawn's
range of movement starting from B3b (m = move, c = capture):

Layer A
4: - c -
3: c m c
2: - c -
1: - - -

Layer B
5: -
4: c m c
3: m p m
2: c m c
1: - - -
0: -

Layer C
4: - c -
3: c m c
2: - c -
1: - - -

Variants

When a piece is captured, it returns immediately to the board in the
player's extension square, if that square is vacant. If the extension square
is occupied, the piece is lost. The idea behind this variant is to extend
what might otherwise be a fairly short game and give rise to more unusual
tactical formations.

Instead of capturing like a Cube+ bishop, the pawn captures along the
3D diagonals:

Layer A
4: c - c
3: - m -
2: c - c
1: - - -

Layer B
5: -
4: - m -
3: m p m
2: - m -
1: - - -
0: -

Layer C
4: c - c
3: - m -
2: c - c
1: - - -

The pawn can move exactly one square in any direction (26 possible
squares from a central square), making it the most mobile piece. However,
it must capture a bishop by moving in a rooklike direction, and capture
a rook by moving in a bishoplike direction. Thus it can threaten a bishop
without being threatened by the bishop, or threaten a rook ditto, but cant
capture either a rook or a bishop when threatened by same. A pawn can only
threaten the king or capture another pawn along the 3D diagonals.